MySQL wait_timeout and Wordpress
wait_timeout is the time mysql will hold a non-interactive connection open for before closing it basically.
So increasing it to 600 seconds could solve your problem, however, if you set it to 600 seconds and you have lots of people running a slow page on your site at the same time you can get to a point where mysql starts refusing connections and then apache will start queueing requests until it subsequently refuses requests and your server takes a dive.
My suggestion would be to try and find out why a single request is taking over 35 seconds because to be honest, that seems a rather long load time on a single page from a blog to me.